Examples of Convergent Sequences - Lec 03 - Sequence and Series

Several examples on R is considered for checking convergence and remark is made on convergent in a metric space.

[aravinthnarayanan]

In 7th problem, without using the neighborhood concept, shall i use the approach as used in 8th problem i.e. 1/infinity is zero. so the limit is 1. So In this case, neighborhood concept is necessary??